What's the Most You Ever Lost on a Coin Toss? By: Gabriel PotterMBA, AIFA® 2017.03.01

A big part of my job is explaining the outperformance or underperformance of an investment manager versus on index or their peers.  If John Doe’s US Large Cap Core stock fund is underperforming the S&P 500 in the current quarter (or year, or even longer), there will be communication between our office and John Doe’s firm trying to figure out why. This is so we can explain the reasons to our client, in person or through our updated due diligence reports.  The best explanations we receive from managers are stories that explain what went right, what went wrong, and how the fund’s team is navigating the current market environment.  The worst, most disheartening explanations for investment underperformance avoid reasoning altogether.  Underperforming investment managers simply look back at their past results, without justification or explanation. 

The bad argument from John Doe portfolio managers usually goes something like this:  “Yes, we underperformed the index in the past twelve months, but look at our history.  More than half of the time, we beat the index in any given quarter.  We just lost 4 quarterly results in a row.  Mathematically speaking, we are due for a turnaround.  Even if you’re flipping a coin – with pure 50/50 odds – getting 5 heads in a row is really unlikely.  We’re even better than that, so we are due for a comeback.”

This is incorrect logic.  If you were to take out a brand new quarter and ask, “what are the odds of getting heads twice in a row?” the odds are 25%.  However, if you were to flip the quarter and get “heads”, and THEN ask, “what are the odds of getting heads again”, the answer it is still 50/50.  In fact, if you were to flip the coin a ninety-nine times and keep getting heads, the odds are still 50/50 for the one-hundredth flip.  (Mind you, if you flipped a coin 99 times and got heads 99 times in a row, I’d be pretty suspicious of that coin.)  Barring any trick coins or similar shenanigans, for a coin flip, the past results do not influence the odds of current events.  This is also known as Gambler’s fallacy. 

In reality, stock market results are more complicated than the results of a coin flip.  There are competing schools of thought which suggest different outcomes of today’s stock market price change based on yesterday’s results.  For instance, there are schools of investment which suggest, if your stock sector is winning, you are more likely to continue winning.  That’s a momentum trade.  Alternatively, there are schools of thought which suggest yesterday’s winners are equally likely to be a winner or loser tomorrow because the change in market price is an instant reaction to any change in information about the company – that’s the fair market hypothesis investor.  Alternatively, there are schools of thought which suggest yesterday’s winners are likely to be tomorrow’s losers because the market price been stretched beyond the underlying data justified by overeager, unsophisticated investors:  that’s a contrarian school of thought.

So yes, John Doe Large Cap Core could be due for a turnaround for a variety of perfectly valid reasons.  Maybe valuations are stretched, or their style wasn’t in favor, or there is some other event which justifies a regression to the mean in terms of performance.  There are reasonable arguments based on market valuations and economic trends which can be supported by historical trends and logic.  However, the justification shouldn’t be based on the Gambler’s fallacy where the odds are reset to 50/50 for every flip of a coin. 









Gabriel Potter

Gabriel is a Senior Investment Research Associate at Westminster Consulting, where he is responsible for designing strategic asset allocations and conducts proprietary market research.

An avid writer, Gabriel manages the firm’s blog and has been published in the Journal of Compensation and Benefits,...

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